I have often wondered why, why YLC never referred to his art as chen style or some type of related name?

My own feeling is that he probably felt what he did was pretty unique and so called his style by other names before becoming known as simple yang style taiji.This question is asked out of curiosity only.

You wrote: “I have often wondered why, why YLC never referred to his art as chen style or some type of related name? My own feeling is that he probably felt what he did was pretty unique and so called his style by other names before becoming known as simple yang style taiji. This question is asked out of curiosity only.”

The martial arts historian Stanley Henning has done some research in this area, and published a short article in Taijiquan Journal (Vol. 2, no. 1, Winter 2001, pp. 6-7) titled “The Origin of the Name ‘Taijiquan’.” He correctly identifies the philosophical term “taiji” as originating in the commentaries to the Book of Changes (I note that the term also appears in the Zhuangzi), but states that “it was not until much later that we find the term ‘taiji’ itself associated with the martial arts, and later still that it appears with the word ‘quan’ (fist or boxing) appended." He notes that a 1784 book by Zhang Kongzhao, _Boxing Classic: Essentials of Boxing_, used the term taiji in a description of footwork. Henning, citing research by Tang Hao and Xu Zhen, states that the name “taijiquan” first appeared in writings attributed to Wu Yuxiang around 1854. In his concluding paragraph, Henning writes, “Philosophizing or intellectualization of the martial arts appears to have been a late-developing phenomenon in Chinese history that evolved along with a broader trend of philosophical thought, one which emphasized combining literary and physical training under a concept of ‘practical learning.’”

Henning does not mention the story recounted by Yang Zhenji, in which the royal tutor Weng Tenghe used the term “taiji” in reaction to witnessing Yang Luchan’s martial performance. I translated that story a few years ago in the link below. Weng did not use the full name “taijiquan,” but his use of the taiji phrase is roughly contemporaneous with the written appearance of the name in Wu Yuxiang’s writings. Yang Zhenji recounts that Weng gave a gift of his personal calligraphy in a scroll in which he uses the taiji phrase in describing Yang’s “consummate skill.” This could be the way that the taiji term came into the Yang tradition, but there is no way of knowing that with certainty. Since Yang Zhenji quoted the scroll, one assumes that the Yang family still possessed it, or had memorized it. It would be interesting to know if it still exists.

Your question seems to be aimed specifically at what Yang Luchan called his art, but we seem to have no direct evidence of Yang Luchan referring to any name at all for the art that he practiced and promoted. By the way, the link below from 2004 begins with a question from you, almost identical to your present question.